Question

1. Write the nth term of the following sequence in terms of the first term of the sequence.
10, 20, 40, . . .
2.Write the nth term of the following sequence in terms of the first term of the sequence.
2, -4, 8, -16, . . .
3. Write the nth term of the following sequence in terms of the first term of the sequence.
a, a + 4, a + 8, . . .

Answer 1

1.) 10, 20, 40, . . . = 10, 10(2), 10(4), . . . = 10, 10(2)^1, 10(2)^2, . . . = 10(2)^(n - 1)

2.) -4, 8, -16, . . . = -4, -4(-2), -4(4) = -4, -4(-2)^1, -4(-2)^2, . . . = -4(-2)^(n - 1)

3.) a, a + 4, a + 8, . . . = a, a + 1(4), a + 2(4) = a + 4(n - 1)